$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 9x + 4$ and $ BC = 6x + 31$ Find $AC$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {9x + 4} = {6x + 31}$ Solve for $x$ $ 3x = 27$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 9({9}) + 4$ $ BC = 6({9}) + 31$ $ AB = 81 + 4$ $ BC = 54 + 31$ $ AB = 85$ $ BC = 85$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {85} + {85}$ $ AC = 170$